They looked out the window just as a New Jersey Transit train rumbled past in the foreground.

“Does that train go underground to Manhattan?” Prokhorov asked.

“Yes. Yes it does,” Vanderbeek answered with a smile.

Prokhorov, wearing a gray pinstriped suit and a gray tie, nodded his head and continued his first tour of the Newark arena. He had purchased the Nets without seeing where they would play their games for the next two or three years, and that always struck me as a little odd.

Sure, his representatives came here from Moscow and watched a preseason game last fall, but still: Who spends a few hundred-million bucks without taking a quick tour of the place?

Then it hit me Monday as he loped through the arena suites and bars — including one appropriately named for a vodka company — and carefully studied the blueprint for the new NBA locker room.

Maybe there is a very good reason his new partners, the ones who needed his billions to make their boondoggle Brooklyn project a reality, decided to wait so long to take the oligarch to the Rock.

Maybe they didn’t want him to see it.

Prokhorov isn’t the second richest man in Russia for making poor business decisions. You had to wonder, as he walked through the pristine building and shot 3-pointers with the city’s charismatic mayor, if the thought at least popped into his sizable noggin. I’m paying how many rubles to build a new arena in Brooklyn when this place is already here?!

If he was thinking it, he certainly wasn’t saying it. He spoke briefly to the press, admitting that he had no idea how nice the arena was but insisting it would be nothing more than a temporary home.

“It’s a great building,” he said. “We’re really happy. It will be a great home for the next two years for our team.”

Atlantic Yards is too far along, with the funding almost in place and the legal problems mostly erased, for Newark to hold out much hope beyond that. Even Mayor Cory Booker, the ultimate Newark optimist, admits the city’s best bet for a long-term basketball franchise is to sell out the building and showcase the potential to another struggling team.

This was the first chance, and it was a success. Prokhorov and his entourage arrived just after 5:30 p.m. in a pair of black Mercedes, receiving a police escort that took them from the city’s border directly into the arena.

The tour was supposed to last 10 minutes, but seeing an opportunity, Vanderbeek took him everywhere. The hockey owner even stopped at one of the Devils team photos in the hallway outside the locker room to point out Slava Fetisov, but Prokhorov pointed him out first.

“There he is,” the Russian said, putting his finger on the face of his friend. “He looks much younger.”

Whenever Vanderbeek wasn’t at his side, Booker usually was. From the time he took office, Booker has understood the impact an NBA team could have on his city’s national image. Monday, he tried to make sure Prokhorov understood the impact it could have on his wallet, too.

“I’ve whispered in his ears as we’re walking along,” Booker said. “Anybody looking to be a part of an asset that’s only going to increase in value would be foolish to overlook the obvious trajectory that Newark is on.”

It is hard to say if Prokhorov saw that opportunity, and if he did, what it might mean. He wore his best poker face, as usual. When asked if he’d consider keeping the team in Newark for the long term, he answered, “Unfortunately, it is part of the business arrangement.”

He was standing near center court of one of the nicest arenas in the country as he spoke. No matter what happens, at least we know this: The man who bought a hole in the ground in Brooklyn sure seemed impressed. Steve Politi may be reached at spoliti@starledger.com, or follow him at Twitter.com/NJ_StevePoliti